 reserve h,h1 for 0-convergent non-zero Real_Sequence,
         c,c1 for constant Real_Sequence;

theorem :: corresponds to INTEGRA7:13
  for f,F be PartFunc of REAL,REAL, I be non empty Interval, r be Real st
   F is_antiderivative_of f,I holds r(#)F is_antiderivative_of r(#)f,I
proof
    let f,F be PartFunc of REAL,REAL, I be non empty Interval, r be Real;
    assume A1: F is_antiderivative_of f,I; then
    r(#)F is_differentiable_on_interval I &
    (r(#)F)`\I = r(#)(F`\I) by FDIFF_12:23;
    hence r(#)F is_antiderivative_of r(#)f,I by A1,RFUNCT_1:49;
end;
